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Aspects of Mathematical Finance
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.
Aspects of Brownian motion
Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum.
Artinian Modules over Group Rings
This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.
Arnolds Problems
Arnold's Problems contains mathematical problems.The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world.The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them).
Aritmetica, crittografia e codici = Arithmetic, cryptography and codes
The basic techniques of algebra and number theory useful in recent applications to cryptography and codes are developed, with the aim of being elementary and self-sufficient. The emphasis is on computational problems. This part of the volume can be useful as a textbook for a first course in algebra for mathematicians, computer scientists or engineers. Important applications of algebra and geometry to cryptography and codes are then illustrated. Both, cryptography and codes have significant applications in daily life which are illustrated here. Cryptography is developed in detail in much of its classic and current aspects, and both private and public key cryptography are developed. Cryptography with the use of elliptic curves on finite fields is also illustrated. A chapter introducing the subject is dedicated to linear codes.
Aritmetica : Un approccio computazionale = Arithmetic : A computational approach
Intended to be a contribution to the algorithmic re-reading of some classic topics of elementary number theory and an invitation to more demanding reading, according to the indications provided by the bibliography annexed to it.
Arithmetical investigations : Representation theory, orthogonal polynomials, and quantum interpolations
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory.
Approval Voting
The book proposes a compelling way to elect some 500,000 officials in public elections. After a generation of discussion and debate on the subject, the authors remain convinced that Approval Voting is as relevant today.
Applied Stochastic Processes
Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusionsThe types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods.The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it.The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations.
Applied Statistics Using SPSS, STATISTICA, MATLAB and R
The book provides a comprehensive coverage of the main statistical analysis topics important for practical applications such as data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics.
Applied Semi-Markov Processes
The book presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. These concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.This book is intended for graduate students and researchers in mathematics, operations research and engineering; it might also appeal to actuaries and financial managers, and anyone interested in its applications for banks, mechanical industries for reliability aspects, and insurance companies.
Applied Quantitative Finance
Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance.
Applied Proof Theory : Proof Interpretations and Their Use in Mathematics
Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpretations) and concerns the extraction of effective data (such as bounds) from prima facie ineffective proofs as well as new qualitative results such as independence of solutions from certain parameters, generalizations of proofs by elimination of premises. The book first develops the necessary logical machinery emphasizing novel forms of Gödel's famous functional ('Dialectica') interpretation. It then establishes general logical metatheorems that connect these techniques with concrete mathematics. Finally, two extended case studies (one in approximation theory and one in fixed point theory) show in detail how this machinery can be applied to concrete proofs in different areas of mathematics.
Applied Probability and Statistics
This text is designed for a one-semester course on Probability and Statistics. The exposition unfolds systematically from an introductory chapter to such topics as random variables and vectors, stochastic processes, estimation, testing and regression. The topics are well chosen and the presentation is enriched by many examples from real life. Following every chapter, the reader will find many original, solved and unsolved problems and hundreds of multiple choice questions, enabling those unfamiliar with the topics to master them. Additionally appealing are the interesting historical notes on the mathematicians mentioned throughout and a useful bibliography. A distinguishing character of the book is the thorough and succinct handling of the various topics.
Applied Partial Differential Equations : A Visual Approach
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables.
Applied Multivariate Statistical Analysis
This book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis.
Applied Mathematical Demography
it focus on applications of demographic models, while extending its scope to matrix models for stage-classified populations.first introduce the life table to describe age-specific mortality, and then use it to develop theory for stable populations and the rate of population increase. This theory is then revisited in the context of matrix models, for stage-classified as well as age-classified populations. Reproductive value and the stable equivalent population are introduced in both contexts, and Markov chain methods are presented to describe the movement of individuals through the life cycle. Applications of mathematical demography to population projection and forecasting, kinship, microdemography, heterogeneity, and multi-state models are considered.
